The dimension of the quantity `(1)/(epsilon_(0)) (e^(2))/(hc)` is (e = charge of electron, h = Planck's constant and c = velocity of light)

Options

A. `[M^(-1)L^(-3)T^(2)A]`
B. `[M^(0)L^(0)T^(0)A^(0)]`
C. `[ML^(3)T^(-4)A^(-2)]`
D. `[M^(-1)L^(-3)T^(4)A^(2)]`

Answer

B

Explanation

`["Energy"]= [(hc)/(lambda)]`
or `[hc]= ["energy"][lambda]= ["force"]["distance"]^(2)`
Also,`["force"]= ([e^(2)])/[(epsilon_(0))["Distance"]^(2)` or `([e^(2)])/([epsilon_(0)])= ["force"]["distance"]^(2)`
`:. [hc]= ([e^(2)])/([epsilon_(0)])` or `[(e^(2))/(epsilon_(0)). (1)/(hc)]= [M^(0)L^(0)T^(0)A^(0)]`